1. Explain the difference between circumscribed angles and inscribed angles in relationship to a circle.
2. Explain, in your own words, the steps required to convert any equation of a circle into standard form be completing the square.
3. Explain/define the following terms, or draw a picture and label the terms.
a. radius
b. diameter
c. chord
d. secant
e. tangent
f. point of tangency
Answers
9514 1404 393
Explanation:
1. Consider the attachment. Angle CDF is a circumscribed angle. It is formed at the intersection of two tangents to the circle. Angles BCE, CBE, and BEC are inscribed angles. Their vertices are on the circle, and they are formed by two chords.
If a chord degenerates to zero length, the ray it represents with respect to an inscribed angle becomes a tangent. That is, angles BCD and ECD can also be considered to be inscribed angles. Similarly, straight angle DFG at tangent point F can be considered to be a degenerate case of both an inscribed angle and a circumscribed angle. (Some authors may not include degenerate cases in their definitions. YMMV)
__
2. The general form of the equation of a circle is ...
Ax² +Ay² +Dx +Ey +F = 0
Any equation of a circle can be put in this form. If we divide by A, this can be written as ...
x² +y² -2hx -2ky +c = 0 . . . . where h = -D/(2A), k = -E/(2A), c = F/A
and the equation can be further transformed to the standard form ...
(x -h)² +(y -k)² = r² . . . . . where r² = h² +k² -c
The last equation is the result of "completing the square" by adding h² and k² to both sides of the second equation shown. The values of h and k are as shown above, given the coefficients of the general form equation.
__
3. Again refer to the attached diagram.
a) a radius is a line segment with the circle center at one end and a point on the circle at the other end. AB and AC are radii.
b) A diameter is a line segment whose ends are on the circle and whose midpoint is the center of the circle. BC is a diameter.
c) A chord is a line segment whose end points lie on the circle. BC, BE, and CE are chords.
d) A secant is a line containing two points of the circle. Lines CG and CE are secants.
e) A tangent is a degenerate case of a secant in which the two points of intersection merge to one point of intersection. It is a line that touches the circle at exactly one point, the point of tangency. DG and DC are tangents.
f) The point of tangency is the single point where a tangent intersects a circle. A radius to the point of tangency (such as AC) is always perpendicular to the tangent line (DC).
Related Questions
3 inches
1.5 inches
1.5 inches
Answers
Answer:
6 inches
Step-by-step explanation:
solve for x (x-2)(x+1)=3x-2 what is x and x
Answers
in the picture will explain the explanation
during the first week of the Season Carly averaged 27 points per basketball game then she went on a scoring streak.
Answers
Answer:
Part a: 7.5
Part B: It changes by 1.5
Step-by-step explanation:
PART A:
In the table you are suppose to find out how much it increases by so you subtract,
[tex]4.5 - 3 = 1.5[/tex]
[tex]6 - 4.5 = 1.5[/tex]
Since we know the difference is 1.5 you will add 6 by 1.5
[tex]6 + 1.5 = 7.5[/tex]
Therefore, the answer is 7.5
PART B: It changes by 1.5 because the difference between the increase in points is 1.5
The results of a survey of 150 students about whether they
own an electronic tablet or a laptop are shown in the two-way
frequency table.
Answers
Answer:
its either quantitive data ( numerical measurements) or categorical data (cannot be expressed using numbers)
Two way frequency table: Pairs categorical values to list frequencies
Step-by-step explanation:
For example: One hundred students were surveyed about which beverage they chose at lunch. Some of the results are shown in the two-way frrequency table below.
Lunch Bevarage
genders Juice. Milk. Water. Total
Girl : 10 13 17 40
Boy: 15 24 21 60
Total: 25 37 38 = 100
3n+14=-4 =?
Please do this this right (my grade depends on it)
Answers
Answer:
Step-by-step explanation:
-6
3n = -18
divide both sides by 3
n = -6
Solve the system of equation by elimination.
x+2y= -7
-x-2y=8
A. (8,7)
B. No solution
C. (-7,8)
D. (-8,7)
If you can, please explain step by step:)
Answers
Answer: D
Step-by-step explanation:
C(x) = 5x^2 + x + 7 and
d(x) = x^2 – 10
d(c(3))
Answers
Answer:
d(c(3))=30I5
Step-by-step explanation:
C(3)=5×9+3 +7=55
d(c(3))= ( 55)^2-10= 3O 15
The range of a relation is given.
-2,-1,0,1,2
Which domain would make the relation not a function?
o 1,1,0,-1, - 1
0 -2, -1,0,1,2
O 0,-1, 2, 1,0
0 0,1,2,3,4
Answers
Answer:
0 -2, -1,0,1,2
Step-by-step explanation:
The difference between two numbers is 8. Twice the number is 4 more than the larger number. What is the smaller number?
Answers
Answer:
If the two numbers are x and y, then:
x + y = 8
18 - 2x = 4y - 2.
When we subtract y from both sides in our first equation we get:
x = 8 - y, so:
18 - 2(8 - y) = 4y - 2
18 - 16 + 2y = 4y - 2
2 + 2y = 4y - 2
2y = 4
y = 2
Since x + y = 8, and y = 2, x = 6, and since 6 > 2, the larger number is 6.
LIM w→(-4) ((sin (pie*w)) /w^2-16)
No answer needed!
Answers
Answer: yes
Step-by-step explanation:
Which is true about the data shown in the scatter plot
Answers
Answer:
d
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Got it right in use test prep
4 × 22 + 16 ÷ 4 - (4.9 + 5.5)
Answers
Answer:
81.6
Step-by-step explanation:
4 × 22 + 16 ÷ 4 - (4.9 + 5.5)
88 + 4 - (10.4)
81.6
Which similarly proves the two triangles are similar?
Answers
Answer:
If their angles are the same, if they are proportional, if it states so
Step-by-step explanation:
I don't see the image you sent, but just naming different things that proves how triangles are similar.
Kensington was selling Girl Scout cookies and a customer offered her a deal. The customer would place three $1 bills, one $5 bill and one $10 bill in a bag. Kensington would reach into the bag and take one bill from the bag and get paid that instead of the $5 it would cost for one box of Girl Scout cookies. Should she take the deal? Or should she insist on getting the regular cost of $5?
Answers
Answer:
no she should take the deal
Step-by-step explanation:
there are 5 bills in that bag and only 1 of them has a chance of being over the regular price where as 3 have a chance of being under the regurla price the odds a not in the girl scouts favor as she has a 60%chance of not getting a $1 and only a 20% chance of getting the $10.
Pleaseee Helppppp
Find the minimum value of the function f(x) = x2 + 12x + 31.5 to the
nearest hundredth.
Answers
Answer:
The answer is pie
Step-by-step explanation:
I know best
Answer:
x = -6.00 (rounded to nearest hundredth)
Step-by-step explanation:
for a quadratic equation, [tex]h(x)=ax^2+bx+c[/tex] we have [tex]f(x)=x^2+12x+31.5[/tex] a = 1 b = 12 to find minimum use equation [tex]x=\frac{-b}{2a}[/tex] [tex]x=\frac{-b}{2a}\\x=\frac{-(12)}{2(1)}\\x=\frac{-12}{2}=-6[/tex](16) In 2008, the number tourists visiting France was 7.94 x 1017. The
number of tourists visiting Italy was 4.27 x 10^7. Find the difference in the
number of visitors
Answers
Answer:
3.67 × 10^7Step-by-step explanation:
Number of tourists visiting France = 7.94 × 10^7Number of tourists visiting Italy = 4.27 × 10^7The difference:
7.94 × 10^7 - 4.27 × 10^7 =(7.94 - 4.27) × 10^7 =3.67 × 10^7 more visitors in Francei need help with this pleasee
Answers
Answers:
angle GFH = 60 degreesangle GHD = 110 degreesangle FGH = 10 degrees================================================
Explanation:
Angle CFG is given to be 120 degrees.
The angle to the right that's adjacent to this is angle GFH. The two angles add to 180
(angle CFG) + (angle GFH) = 180
(120) + (angle GFH) = 180
angle GFH = 180 - 120
angle GFH = 60 degrees
-----------------------
Angle XGA is 70 degrees. Note how it corresponds to angle XHC since both angles are in the same northwest quadrant of their four-corner angle configuration.
Corresponding angles are congruent due to the parallel lines AB and CD.
This means angle XHC is also 70 degrees.
We'll use the same idea as in the last section
(angle XHC) + (angle GHD) = 180
(70) + (angle GHD) = 180
angle GHD = 180 - 70
angle GHD = 110 degrees
--------------------
Focus on triangle FGH.
We want to find angle FGH, which is the same as angle G when focusing solely on triangle FGH and no other points or triangles.
In the previous two sections, we found
angle GFH = 60angle XHC = 110This can be shortened to
angle F = 60angle H = 110Again we must focus solely on triangle FGH and nothing else.
So we have
angle F = 60angle G = unknownangle H = 110Let's solve for G
F+G+H = 180 .... angles of a triangle always add to 180
60+G+110 = 180
G+170 = 180
G = 180-170
G = 10
For triangle FGH, angle G is 10 degrees.
This means angle FGH is 10 degrees.
The equation (x – 5)2 = –2(y + 1) represents a parabola. Complete the statements describing the graph.
The vertex is
(5,1)
(5,-1)
(-5,1)
(-5,-1)
The graph opens
up
left
right
down
Answers
Answer:
(5,-1)
Step-by-step explanation:
TAKE ONE SIDE
(X-5)2=0
2X-10= 0
2X=10
X=10/2
X=5
THEN TAKE OTHE SIDE
-2(y+1) =0
-2y-2=0
-2y=2
y=2/-2
y=-1
So the answer is (5,-1)
And it should be in right down
(-5,1) , the graph opens down
What is an equation?
'An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.'
.Given equation: 2(x-5) = -2(y+1)
Evaluating left-hand side,
⇒ (x-5)2 = 0
⇒2x-10 = 0
⇒2x = 10
⇒x =10/2
⇒x = 5
Evaluating RHS,
⇒-2(y+1) = 0
⇒-2y-2 = 0
⇒-2y = 2
⇒y = 2/-2
⇒y = -1
Hence, we can conclude the vertex is at (-5,1) and the graph opens down.
Learn more about graphs here: https://brainly.com/question/4074088
#SPJ2
Solve 4x+34 help please
Answers
9514 1404 393
Answer:
78
Step-by-step explanation:
The base (JL) is twice the length of the midline (MN), so you have ...
4x +34 = 2(5x -16)
4x +34 = 10x -32 . . . eliminate parentheses
66 = 6x . . . . . . . . add 32-4x
11 = x
Then the length of JL is ...
4(11) +34 = 78
Which situation represents a proportional relationship?
А.
The cost of purchasing t-shirts for $5.80 each.
B
The cost of purchasing belts for $11.00 each with a delivery charge of $3.50.
С.
The cost of purchasing a box of socks for $1.75 per sock plus $2.15 for the box.
D
The cost of purchasing pants for $21.50 each with a coupon for $3.25 off the total cost.
Answers
Answer:
С.
Step-by-step explanation:
From the options provided the only one that represents a proportional relationship was The cost of purchasing a box of socks for $1.75 per sock plus $2.15 for the box. This is because the total cost of the boxes depends on the number of socks that are bought since every pair of socks that are bought comes with a box which causes the total costs of the boxes to increase. Therefore, the number of sock pairs and the number of boxes has a proportional relationship.
What does a cluster tell you about the data on a scatter plot?
Answers
Answer:
it all depends on where it is if it is in the middle you do not have enough information to determine if it is increasing or decreasing
Step-by-step explanation:
how 2 explain this?
Thanksss.
Answers
Explanation: I would substitute 2 into x which would be y = 2(2) + 3. I would then multiply 2 and 2 which would give me 4 and then add 3 which I get 7. This means that (2,5) is not a solution to the equation.
Ronald repairs computers. He charges $25 for a house call and $24 per hour. If Ronald charges $145 for one of his jobs, including the house call, which equation can be used to find h, the number of hours he worked?
Answers
Answer:
25+24h=145
Step-by-step explanation:
Two oranges and five lemons cost $2.95. Three oranges and two lemons cost $2.50. How
much would five oranges and three lemons cost?
Answers
Answer:
40 p
Step-by-step explanation:
2.50 plus 40 equal 2.90 and that is how u get ur answer
Ethan has saved $180 to buy a bicycle which costs $540. He wants to find how much more he needs to save to buy the bicycle
Which equation when solved would show Ethan the amount of money he needs to save?
Answers
Answer:
X = 360
Step-by-step explanation:
180 + x = 540
-180 = -180
Answer:
540-180=360
Step-by-step explanation:
Why? Because he has 180, he need 540. There is 360 in between, which is the money he needs.
Hope this is the right equation.
Where is most of Earth’s fresh water found?
in the ground
near the poles
in lakes and streams
in the air as water vapor
Answers
Answer:
B: near the poles
Step-by-step explanation:
got it right on edge 2020
Answer:
near the poles
Step-by-step explanation:
trust me I know
1. What is the solution of n^2-49=0?
a.-7
b.7
c.+7
d. no solution
2.What is the solution of x^2+64=0?
a.-5
b.8
c.+8
d.no solution
3.What is the side length of a square with an area of 144x^2?
a.12
b.12x
c.+12x
d.no solution
4.What is the value of z so that -9 and 9 are both solutions of x^2+z=103?
a.-22
b.3
c.22
d.184
Answers
Answer:
it would be d for #1 because it has no solution for the question
please help
Solve |6k + 12| + 9 = 9 for k
Answers
Answer:
k = -1/2
Step-by-step explanation:
|6k + 12| + 9 =9
6k + 12 = 9-9
6k + 12 = 0
6k = -12
k = -1/2
(m²+mn+n²)(m²-mn+n²)
Answers
Answer:
[tex]m^{4\\}[/tex]+[tex]m^{2}[/tex][tex]n^{2}[/tex]+[tex]n^{4}[/tex]
Step-by-step explanation:
If you're distributing each value, I would recommend you to use the lattice method so that you can work on it faster. Make sure to add the exponents instead of multiplying to have an accurate answer. Once your done then cross out the ones that would subtract to 0 which would leave you with [tex]m^{4\\}[/tex]+[tex]m^{2}[/tex][tex]n^{2}[/tex]+[tex]n^{4}[/tex] as your final answer if you did it properly.
What is the value of the expression when a = 5, b = 4 , and c = 6?
4a/2b−c
2
5
9
10
Answers
Step-by-step explanation:
9 +6=15-6=9
so your answer should be 9
mark me brainliest lol
Answer:
now you can say as brainliest to other person :)